The Method of Lie Series for Differential Equations and Its Extensions.
Final technical rept.,
INNSBRUCK UNIV (AUSTRIA) INST OF MATHEMATICS
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The work considers the initial value problem for an ordinary differential equation in a Banach space. The starting point of this research is Grobners notation, the so-called Lie series. An explicit computation of the two normal subgroups whose product is the orthogonal group and its transform is given. A general method for the numerical integration of ordinary differential equations is studied. This method includes in special cases the multi-step methods, Runge-Kutta methods multistage, Taylor series multi derivative and their extensions. Finally, Eulers Runge-Kutta methods of type IIIc are considered and their A-stability is proved. The implicit Eulers method is studied and is shown to be highly stable. An algorithm is implemented and numerical results are given. Author
- Theoretical Mathematics